Second- and fourth-order-accurate spatial discretization methods give rise to discretization errors which are large than the corresponding subgrid terms in large eddy simulation of compressible shear layers in 2D, if the ratio between the filter width and the grid spacing is close to one. Even if an exact representation for the subgrid-scale contributions is assumed, large eddy simulation is accurate only if this ratio is sufficiently larger than one. In that regime fourth-order methods are more accurate than second-order methods. An analysis of the data obtained from two-dimensional direct numerical simulations of compressible shear layers substantiates these assertions.